Question

when these two dice are rolled, what is the probability that the number rolled on die a will be greater than the number rolled on die b?

Answer 1

Answer: 5/12

Step-by-step explanation

Let's say a "3" is rolled on cube A. That would mean cube B would need to roll a "1" or "2", so the result of A is larger than B.

This idea is applied to the other possible rolls to generate this table.

`\begin{array}c \cline{1-2}A & \ \ \ \ \ \ \ \ B\\\cline{1-2}1 & 0\\\cline{1-2}2 & 1\\\cline{1-2}3 & \text{1 and 2}\\\cline{1-2}4 & \text{1, 2, and 3}\\\cline{1-2}5 & \text{1, 2, 3, and 4}\\\cline{1-2}6 & \text{1, 2, 3, 4, and 5}\\\cline{1-2}\end{array}`

We have 1+2+3+4+5 = 15 different cases where the result of A is larger than the result of B. This is out of 6*6 = 36 ways to roll two dice.

Therefore, we have a probability of 15/36 = 5/12 where A > B.

5/12 = 0.4167 = 41.67% approximately